Explicit construction of a Chern–Moser connection for CR manifolds of codimension two
Copyright policy )Explicit construction of a Chern–Moser connection for CR manifolds of codimension two
In the present paper we suggest an explicit construction of a Cartan connection for an elliptic or hyperbolic CR manifold M of dimension six and codimension two, i.e. a pair (P, w), consisting of a principal bundle P over M and of a Cartan connection form w on P, satisfying the following property: the (local) CR transformations of M are in one to one correspondence with the (local) automorphisms of P which preserve w. For any point x in M, this construction determines an explicit immersion of the stability subalgebra Lie(aut(M)_x) into the Lie algebra Lie(H) of the structure group H of P.
40 pages - This is a revised version in which a misuse of formula (6.10) of the old version in the following computations has been corrected - the changes starts only from pag. 24 and do not concerns the line of arguments
- University of New England Australia
- University of Camerino Italy
- University of New England United States
Mathematics - Differential Geometry, 32V05 (Primary), 53A55 (Secondary), CR structures, CR operators, and generalizations, Mathematics - Complex Variables, 32V05 (Primary); 53C15; 53A55 (Secondary), 53C15, Differential Geometry (math.DG), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, CR manifolds of higher codimension, invariants for CR structures, Complex Variables (math.CV)
Mathematics - Differential Geometry, 32V05 (Primary), 53A55 (Secondary), CR structures, CR operators, and generalizations, Mathematics - Complex Variables, 32V05 (Primary); 53C15; 53A55 (Secondary), 53C15, Differential Geometry (math.DG), General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, CR manifolds of higher codimension, invariants for CR structures, Complex Variables (math.CV)
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